Answer:
[tex]\large\boxed{\sqrt{100x^3}=10x\sqrt{x}}[/tex]
Step-by-step explanation:
[tex]Domain:\ x\geq0\\\\\sqrt{100x^3}=\sqrt{10^2x^{2+1}}\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt{10^2\cdot x^2\cdot x^1}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{10^2}\cdot\sqrt{x^2}\cdot\sqrt{x}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=10\cdot x\cdot\sqrt{x}=10x\sqrt{x}[/tex]
